Vacuum energy in some particular quantum field theories

TL;DR

This paper investigates a class of quantum field theories, including supersymmetric models, showing that their vacuum energy is zero due to their scaling properties and associated energy-momentum tensor.

Contribution

It demonstrates that theories with equal numbers of commuting and anti-commuting fields have zero vacuum energy, highlighting a fundamental property related to their scaling behavior.

Findings

Vacuum energy is zero in these theories.

Scaling properties determine the vacuum energy.

Supersymmetric models are included in the analysis.

Abstract

We study the properties of a class of quantum field theories endowed with an equal number of anti commuting and commuting field variables, the most common example being the supersymmetric models. Based on the scaling properties of the partition function we find that these theories have the quantum energy momentum tensor associated to dilatations and thus the vacuum energy equal to zero.